A129488 Smallest odd prime dividing binomial(2n,n).

3, 5, 5, 3, 3, 3, 3, 5, 11, 3, 7, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 7, 5, 3, 7, 7, 3, 3, 3, 3, 7, 7, 3, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 3, 5, 5, 3, 3, 3, 3, 5, 5, 3, 5, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset: 2

Author

T. D. Noe, Apr 17 2007

Keywords

• nonn

Comments

The Erdős paper calls this function g(n) and states that it is not known whether it is bounded. Currently, g(3160)=13 is the greatest known value of g. See A129489.

Links

• T. D. Noe, Table of n, a(n) for n = 2..5000
• P. Erdős, R. L. Graham, I. Z. Russa and E. G. Straus, On the prime factors of C(2n,n), Math. Comp. 29 (1975), 83-92.

Crossrefs

Cf. A030979 (n such that g(n)>=11), A129489, A266366.

Programs

Mathematica

Table[Transpose[FactorInteger[Binomial[2n,n]]][[1,2]], {n,2,150}]

PARI

a(n)=my(k);forprime(p=3,default(primelimit),k=1;while((k*=p)<=2*n,if(n/k-n\k>1/2,return(p)))) \\ Charles R Greathouse IV, Dec 19 2011